What is Google Sites and who is it for?
Google Sites (both classic and new) is best understood as a way to build collaborative websites and intranets that integrate Google Apps, Docs, Drive, Calendar, Maps, Forms and more.
Google Sites has lots of collaboration tools built-in— such as permissions and collaborative documents. This makes it a natural intranet builder. To take advantage of this your organization should already use Google Apps (though not necessary).
You'll be frustrated if you try to use Google Sites for building a business website. It's just not meant for that. Sure you could try to make it work— it's free after all— but you'll almost certainly be frustrated. The themes are too simple and feature set is just not designed around that.
Google Sites is best suited for building collaborative websites and intranets that connect Google products. Follow this rule and you'll be happy.